Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  a : sigma
        (λ index : sigma (λ _ : list A, list A),
           All2_fold P (pr1 index) (pr2 index))
  b : sigma
        (λ index : sigma (λ _ : list A, list A),
           All2_fold P (pr1 index) (pr2 index))
  H : NoConfusion_All2_fold A P a b
  ============================
   (a = b)


DEBUG:Going to execute:
intros;
            match goal with
            | |- ?R ?a ?b =>
                  CoreTactics.destruct_sigma a; CoreTactics.destruct_sigma b;
                   destruct a; DepElim.depelim b; 
                   simpl in * |-;
                   CoreTactics.on_last_hyp
                    ltac:(fun id =>
                            hnf in id;
                             CoreTactics.destruct_tele_eq id || destruct id);
                   (solve [ constructor ])
            | |- ?f ?a ?b _ = _ => solve_noconf_inv_eq a b
            end